Constant rate crystal polymers

The polymer crystallization depends sensitively on the temperature Tc at which it occurs, more precisely on the degree of undercooling A T=Tm-Tc below the melting temperature Tm. Since we have to estimate Tm, at least roughly, of our lamellar crystal model, we first study the melting process of a lamella during the temperature increase at a constant rate. 

Once primary nuclei are formed the ensuing spherulites grow radially at a constant rate. Primary crystallization, which occurs initially on the surface of the primary nucleus and then on the surface of the growing lamellar, also involves a nucleation step, secondary nucleation. It is this step that largely governs the ultimate crystal thickness and which forms the focus of most kinetic theories of polymer crystallization. 

When a polymer melt is cooled below T, crystallization is initiated at nuclei (often minute specks of impurity) at different points in the melt. The crystallization proceeds by the growth of the spherulites, which at this stage are spherical, each spherulite having a nucleus at its centre (see Figure 2.7). The spherulite expands at a constant rate if the temperature is... 

It was often found that, contrary to the theoretical prediction, the value of n is noninteger (Avrami 1939). The Avrami model is based on several assumptions, such as constancy in shape of the growing crystal, constant rate of radial growth, lack of induction time, uniqueness of the nucleation mode, complete crystallinity of the sample, random distribution of nuclei, constant value of radial density, primary nucleation process (no secondary nucleation), and absence of overlap between the growing crystallization fronts. These assumptions are often not met in polymer (blend) crystallization. Also, erroneous determination of the zero time and an overestimation of the enthalpy of fusion of the polymer at a given time can lead to noninteger values for n (Grenier and Prud homme 1980). 

DSC is a widely used thermal analysis technique for studying polymer crystallization. DSC instruments contain two sample holders, each connected to their own heat source. A polymer sample is placed in one of the holders, while the other sample holder is left empty as a reference cell. By changing the temperature of both holders at a constant rate, the difference in the energy extracted from both holders to keep them at the same temperature is recorded. 

The Deformation History. Polymer dynamics can be investigated by SANS via special phenomena such as demixtion observed by X-rays or crystallization. A more direct way is simply to observe a sample mechanically displaced out of equilibrium. A classical approach used in other techniques is a steady deformation, characterised by a constant rate of deformation s = 1/L dL/dt, where L is a distance. The investigation in time is related to the dependence on s. Other procedures involve time-dependent deformation histories, which relate to the actual time typical cases are a periodic deformation, e.g. oscillatory, and a stepstrain deformation. A time analysis is then needed. In the case of a periodic deformation, one can divide the period 2nj into small intervals of phase v /, i / -I- A , within which is measured. In the case of... 

When a compound crystallizes from solution, the crystals may contain solvent of crystallization. The compound is then called a solvate, and if the solvent is water, the compound is a hydrate. The presence of the solvent is revealed by elemental analysis, and thermogravimetric analysis (TGA) shows whether the solvent molecules are loosely or strongly bound in the crystal lattice. More generally, TGA is used to investigate the thermal degradation of inorganic compounds or polymers or the gas uptake of a solid (e.g. H2 uptake by WO3). A TGA instrument is able to simultaneously heat (at a constant rate) and record the mass of a sample. Samples are usually heated in air or N2, or in an... 

Nonisothermal Melt Crystallization. In routine DSC crystallization measurements of polymers, nonisothermal crystallization is typically used.This method is simple and gives practical results. At the same time, the information obtained is limited to the characteristic temperatures of crystallization. The sample is heated beyond the equilibrium melting point of the polymer, held there for several minutes for temperature equilibration, and also to destroy all nuclei, and then it is cooled at a specific constant rate to room temperature or below to record the crystallization exotherm. 

Another characteristic of liquid crystal polymer systems is the dependence of viscosity on the shear stress t. Viscosity of complex systems decreases with increasing stress in the range of small shear rates. With further increase in stress the viscosity remains constant in a certain interval of t and then decreases again. 

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